A penthouse atop a new Miami Beach tower designed by architect Renzo Piano is coming on the market for $68 million. If it sells for close to that number, it would be the most expensive apartment ever sold in Florida, according to the developer.

The current record is the $60 million sale of a penthouse at Miami’s Faena House condominium to hedge fund executive Ken Griffin in 2015, public records show. Since then, the Miami market has softened significantly, according to people familiar with the market.

The new Miami Beach tower is the first in the U.S. for architect Renzo Piano, who is known for designing buildings like the Shard, an office and residential skyscraper in London, and the Centre Georges Pompidou in Paris.

Laura Stevens for The Wall Street Journal

David Martin, president of Miami-based Terra, which developed the new building in partnership with Bizzi & Partners Development, New Valley and Pacific Eagle, said the $68 million price tag is justified by the scale of the property and the vast outdoor space. The unit is expected to have 12,410 square feet of interior space and 18,247 square feet of outdoor terraces, including a private rooftop area, according to Terra. There will be six bedrooms.

The penthouse will also have its own gym, two private elevators, a home movie theater, a Turkish hammam, a putting green, two outdoor kitchens and two 45-foot-long infinity pools on either side of the unit for swims at sunrise and sunset. There will be 360-degree views of the ocean and downtown Miami, as well as of a 35-acre park next door.

A rendering of a unit. A penthouse atop the under-construction project is coming on the market for $68 million.

Eighty Seven Park (Rendering)

The project, known as Eighty Seven Park, is one of the first in the U.S. for Mr. Piano, who is known for designing buildings like the Shard, an office and residential skyscraper in London, and the Centre Georges Pompidou in Paris. Construction on the 18-story condo tower began in 2017 on the site of the former Biltmore Terrace Hotel, and will be completed by the third quarter of 2019, Mr. Martin said.

Mr. Martin said 54 of the project’s 66 units are in contract, despite the slowdown in the market. He said the pool has shifted toward domestic buyers in recent months. Douglas Elliman is leading sales.